Fethi Bin Muhammad Belgacem

Model of platelet transport in flowing blood with drift and diffusion terms.

A drift term is added to the convective diffusion equation for platelet transport so that situations with near-wall excesses of platelets can be described. The mathematical relationship between the drift and the fully developed, steady-state platelet concentration profile is shown and a functional form of the drift that leads to concentration profiles similar to experimentally determined profiles is provided. The transport equation is numerically integrated to determine concentration profiles in the developing region of a tube flow. With the approximate drift function and typical values of augmented diffusion constant, the calculated concentration profiles have near-wall excesses that mimic experimental results, thus implying the extended equation is a valid description of rheological events. Stochastic differential equations that are equivalent to the convective diffusion transport equation are shown, and simulations with them are used to illustrate the impact of the drift term on platelet concentration profiles during deposition in a tube flow.

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7.

A New Equation Relating the Viscosity Arrhenius Temperature and the Activation Energy for Some Newtonian Classical Solvents

In transport phenomena, precise knowledge or estimation of fluids properties is necessary, for mass flow and heat transfer computations. Viscosity is one of the important properties which are affected by pressure and temperature. In the present work, based on statistical techniques for nonlinear regression analysis and correlation tests, we propose a novel equation modeling the relationship between the two parameters of viscosity Arrhenius-type equation, such as the energy () and the preexponential factor (). Then, we introduce a third parameter, the Arrhenius temperature (), to enrich the model and the discussion. Empirical validations using 75 data sets of viscosity of pure solvents studied at different temperature ranges are provided from previous works in the literature and give excellent statistical correlations, thus allowing us to rewrite the Arrhenius equation using a single parameter instead of two. In addition, the suggested model is very beneficial for engineering data since it would permit estimating the missing parameter value, if a well-established estimate of the other parameter is readily available.

Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations

We make use of the so-called Sumudu transform method (STM), a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions.

Analytical solutions for nonlinear long–short wave interaction systems with highly complex structure

Abstract In this paper, we investigate and use the new modified exp ( − Ω ( ξ ) ) -expansion method, (MEM). We apply the new MEM to nonlinear long–short-wave interaction systems (NLSWIS). Among our findings are sets of solutions including, but not limited to, new hyperbolic, complex, and dark soliton solutions. Not only is MEM shown to be highly adaptable for partial differential equations with strong nonlinearities, but also, it turns out to be highly efficient, despite its ease.

A distinctive Sumudu treatment of trigonometric functions

Abstract The Sumudu transform integral equation is solved by continuous integration by parts, to obtain its definition for trigonometric functions. The transform variable, u , is included as a factor in the argument of f ( t ) , and summing the integrated coefficients evaluated at zero yields the image of trigonometric functions. The obtained result is inverted to show the expansion of trigonometric functions as an infinite series. Maple graphs, tables of extended Sumudu properties, and infinite series expansions of trigonometric functions Sumudi images are given.

Mathematical analysis of the Generalized Benjamin and Burger-Kdv Equations via the Extended Trial Equation Method

Abstract In this paper, using the Extended Trial Equation (ETEM), we get new traveling wave solutions of the Generalized Benjamin, the Generalized Burger-Kdv Equations (GBE, GBKE). The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and moreover investigated. Furthermore, to concretely enrich this research production, we provide illustrative, Mathematica Release 7 based, 3D graphics of the gotten solutions, with well chosen, yet structure revealing parameters.

CONNECTIONS BETWEEN THE CONVECTIVE DIFFUSION EQUATION AND THE FORCED BURGERS EQUATION

The convective diffusion equation with drift b(x) and indefinite weight r(x), ∂ϕ∂t=∂∂x[a∂ϕ∂x−b(x)ϕ]

Advances in the Natural transform

The literature review of the Natural transform and the existing definitions and connections to the Laplace and Sumudu transforms are discussed in this communication. Along with the complex inverse Natural transform and Heavisides expansion formula, the relation of Bessels function to Natural transform (and hence Laplace and Sumudu transforms) are defined.

Application of the Novel (G′/G)-Expansion Method to the Regularized Long Wave Equation

Abstract In this paper we investigate the regularized long wave equation involving parameters by applying the novel (G′/G)-expansion method together with the generalized Riccati equation. The solutions obtained in this manuscript may be imperative and significant for the explanation of some practical physical phenomena. The performance of this method is reliable, useful, and gives us more new exact solutions than the existing methods such as the basic (G′/G)-expansion method, the extended (G′/G)-expansion method, the improved (G′/G)-expansion method, the generalized and improved (G′/G)-expansion method etc. The obtained traveling wave solutions including solitons and periodic solutions are presented through the hyperbolic, the trigonometric and the rational functions. The method turns out to be a powerful mathematical tool and a step foward towards, albeit easily and yet efficiently, solving nonlinear evolution equations.